On the Symmetric Gaussian Multiple Description Rate-Distortion Function

We consider symmetric multiple description coding for the Gaussian source, and provide upper and lower bounds for the individual description rate-distortion function. One of the main contributions of this work is a novel lower bound on the sum rate under symmetric distortion constraints, which yields a lower bound on the individual rate for the symmetric case. Two upper bounds are derived, the first of which is based on successive refinement coding coupled with multilevel diversity coding (SR-MLD), and the second is based on the multi-layer coding scheme proposed in literature. We show that the gaps between the lower bound and the upper bounds are no larger than certain constants depending only on the number of descriptions, but not the distortion constraints. Moreover, regardless of the number of descriptions, the gap between the lower bound and the upper bound using the SR-MLD coding scheme is less than 1.5 bits, and for the other case, the gap is less than 1 bit.